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<html>
<head>
<title>
TRIANGULATION_TRIANGLE_NEIGHBORS - Triangle Neighbors
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TRIANGULATION_TRIANGLE_NEIGHBORS <br>
Triangle Neighbors <br>
in a Triangulation
</h1>
<hr>
<p>
<b>TRIANGULATION_TRIANGLE_NEIGHBORS</b>
is a MATLAB program which
computes the three
neighboring triangles of each triangle in a triangulation.
</p>
<p>
The user supplies a node file and a triangle file, containing
the coordinates of the nodes, and the indices of the nodes that
make up each triangle. Either 3-node or 6-node triangles may
be used.
</p>
<p>
The program reads the data, computes the triangle neighbor information,
and writes out the information to a file. In cases where one side
of a triangle has no triangle neighbor, a value of -1 is assigned.
</p>
<p>
The triangle neighbor array is useful if the triangulation has
to be searched to find the triangle containing a given point.
It is also useful when analyzing the bandwidth of the adjacency
matrix, or of a finite element matrix derived from the triangulation.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>triangulation_triangle_neighbors</b> ( <i>'prefix'</i> )
</blockquote>
where <i>'prefix'</i> is the common prefix for the node and triangle files,
and will also be used to name the output file:
<ul>
<li>
<i>'prefix'</i><b>_nodes.txt</b>, the node coordinates (input);
</li>
<li>
<i>'prefix'</i><b>_elements.txt</b>, the triangulation (input);
</li>
<li>
<i>'prefix'</i><b>_element_neighbors.txt</b>, the triangle neighbors (output);
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TRIANGULATION_TRIANGLE_NEIGHBORS</b> is available in
<a href = "../../c_src/triangulation_triangle_neighbors/triangulation_triangle_neighbors.html">a C version</a> and
<a href = "../../cpp_src/triangulation_triangle_neighbors/triangulation_triangle_neighbors.html">a C++ version</a> and
<a href = "../../f_src/triangulation_triangle_neighbors/triangulation_triangle_neighbors.html">a FORTRAN90 version</a> and
<a href = "../../m_src/triangulation_triangle_neighbors/triangulation_triangle_neighbors.html"> a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/mesh_bandwidth/mesh_bandwidth.html">
MESH_BANDWIDTH</a>,
a MATLAB program which
returns the geometric bandwidth associated with a mesh of
elements of any order and in a space of arbitrary dimension.
</p>
<p>
<a href = "../../m_src/mesh_to_xml/mesh_to_xml.html">
MESH_TO_XML</a>,
a MATLAB program which
reads information defining a 1D, 2D or 3D mesh, namely
a file of node coordinates and a file of elements defined by
node indices, and creates a corresponding XML file for input
to DOLFIN or FENICS.
</p>
<p>
<a href = "../../m_src/neighbors_to_metis_graph/neighbors_to_metis_graph.html">
NEIGHBORS_TO_METIS_GRAPH</a>,
a MATLAB program which
reads a triangle mesh neighbor file created by <b>TRIANGULATION_TRIANGLE_NEIGHBORS</b>
and writes a modified version of the same data suitable for input
to the mesh partitioning program METIS.
</p>
<p>
<a href = "../../m_src/rcm/rcm.html">
RCM</a>,
a MATLAB library which
uses the reverse Cuthill-McKee method for mesh renumbering.
</p>
<p>
<a href = "../../f_src/table_delaunay/table_delaunay.html">
TABLE_DELAUNAY</a>,
a FORTRAN90 program which
triangulates nodes whose coordinates are stored in a file.
</p>
<p>
<a href = "../../m_src/tet_mesh_rcm/tet_mesh_rcm.html">
TET_MESH_RCM</a>,
a MATLAB library which
applies the reverse Cuthill-McKee reordering to a tetrahedral
mesh of nodes in 3D.
</p>
<p>
<a href = "../../c_src/triangle/triangle.html">
TRIANGLE</a>,
a C program which
computes a triangulation of a geometric region.
</p>
<p>
<a href = "../../m_src/triangulation/triangulation.html">
TRIANGULATION</a>,
a MATLAB library which
carries out various operations on order 3 ("linear") or order 6
("quadratic") triangulations.
</p>
<p>
<a href = "../../m_src/triangulation_boundary_edges/triangulation_boundary_edges.html">
TRIANGULATION_BOUNDARY_EDGES</a>,
a MATLAB program which
reads data defining a triangulation, determines which edges
lie on the boundary, organizes them into connected components,
and writes this information to a file.
</p>
<p>
<a href = "../../m_src/triangulation_boundary_nodes/triangulation_boundary_nodes.html">
TRIANGULATION_BOUNDARY_NODES</a>,
a MATLAB program which
reads data defining a triangulation, determines which nodes
lie on the boundary, and writes their coordinates to a file.
</p>
<p>
<a href = "../../m_src/triangulation_corner/triangulation_corner.html">
TRIANGULATION_CORNER</a>,
a MATLAB program which
patches triangulations so that no triangle has two sides on the boundary.
</p>
<p>
<a href = "../../m_src/triangulation_delaunay_discrepancy/triangulation_delaunay_discrepancy.html">
TRIANGULATION_DELAUNAY_DISCREPANCY</a>,
a MATLAB program which
measures the amount by which a triangulation fails the local Delaunay test;
</p>
<p>
<a href = "../../m_src/triangulation_display/triangulation_display.html">
TRIANGULATION_DISPLAY</a>,
a MATLAB program which
displays the nodes and elements of a triangulation on the MATLAB graphics screen;
</p>
<p>
<a href = "../../cpp_src/triangulation_display_opengl/triangulation_display_opengl.html">
TRIANGULATION_DISPLAY_OPENGL</a>,
a C++ program which
reads files defining a triangulation and displays an image using Open GL.
</p>
<p>
<a href = "../../m_src/triangulation_histogram/triangulation_histogram.html">
TRIANGULATION_HISTOGRAM</a>,
a MATLAB program which
computes histograms of data over a triangulation.
</p>
<p>
<a href = "../../m_src/triangulation_l2q/triangulation_l2q.html">
TRIANGULATION_L2Q</a>,
a MATLAB program which
reads data defining a 3-node triangulation and generates
midside nodes and writes out the corresponding 6-node triangulation.
</p>
<p>
<a href = "../../m_src/triangulation_mask/triangulation_mask.html">
TRIANGULATION_MASK</a>,
a MATLAB program which
takes an existing triangulation and deletes triangles and
their corresponding nodes as requested by the user.
</p>
<p>
<a href = "../../data/triangulation_order3/triangulation_order3.html">
TRIANGULATION_ORDER3</a>,
a directory which
contains a description and
examples of order 3 triangulations.
</p>
<p>
<a href = "../../data/triangulation_order6/triangulation_order6.html">
TRIANGULATION_ORDER6</a>,
a directory which
contains a description and
examples of order 6 triangulations.
</p>
<p>
<a href = "../../m_src/triangulation_orient/triangulation_orient.html">
TRIANGULATION_ORIENT</a>,
a MATLAB program which
reads data defining a triangulation, makes sure that
every triangle has positive orientation, and if not, writes a
corrected triangle file.
</p>
<p>
<a href = "../../m_src/triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>,
a MATLAB program which
reads data defining a triangulation and creates a
PostScript image of the nodes and triangles.
</p>
<p>
<a href = "../../m_src/triangulation_q2l/triangulation_q2l.html">
TRIANGULATION_Q2L</a>,
a MATLAB program which
reads data defining a 6-node triangulation, and subdivides
each triangle into 4 3-node triangles, writing the resulting
triangulation to a file.
</p>
<p>
<a href = "../../m_src/triangulation_quad/triangulation_quad.html">
TRIANGULATION_QUAD</a>,
a MATLAB program which
estimates the integral of a function over a triangulated region.
</p>
<p>
<a href = "../../m_src/triangulation_quality/triangulation_quality.html">
TRIANGULATION_QUALITY</a>,
a MATLAB program which
reads data defining a triangulation and computes a number
of quality measures.
</p>
<p>
<a href = "../../m_src/triangulation_rcm/triangulation_rcm.html">
TRIANGULATION_RCM</a>,
a MATLAB program which
can reorder the nodes of
a triangulation so that the bandwidth of the associated adjacency
matrix is reduced.
</p>
<p>
<a href = "../../m_src/triangulation_refine/triangulation_refine.html">
TRIANGULATION_REFINE</a>,
a MATLAB program which
reads data defining a triangulation, replaces each triangle
by four congruent smaller ones, and writes the new triangulation
information to a file.
</p>
<p>
<a href = "../../c_src/trig_to_neib/trig_to_neib.html">
TRIG_TO_NEIB</a>,
a C program which
reads "NODE" and "ELE" files (a format prescribed by <b>triangle</b>)
describing a triangulation, and produces a file defining the
neighbor triangles of each element; the program can also produce
information about the Voronoi diagram. The program is by Lili Ju.
</p>
<p>
<a href = "../../m_src/voronoi_neighbors/voronoi_neighbors.html">
VORONOI_NEIGHBORS</a>,
a MATLAB program which
is given a set of points in the plane and determines the
Voronoi adjacency structure, that is, which points share an
edge of the Voronoi diagram.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Marc deBerg, Marc Krevald, Mark Overmars,
Otfried Schwarzkopf,<br>
Computational Geometry,<br>
Springer, 2000,<br>
ISBN: 3-540-65620-0.
</li>
<li>
Joseph ORourke,<br>
Computational Geometry,<br>
Second Edition,<br>
Cambridge, 1998,<br>
ISBN: 0521649765,<br>
LC: QA448.D38.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "triangulation_triangle_neighbors.m">
triangulation_triangle_neighbors.m</a>,
is the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>BIG_CAVITY</b> is a triangulation using 8,195 nodes and 4,000 elements.
<ul>
<li>
<a href = "../../datasets/triangulation_order3/big_cavity_nodes.txt">
big_cavity_nodes.txt</a>,
the node coordinates.
</li>
<li>
<a href = "../../datasets/triangulation_order3/big_cavity_elements.txt">
big_cavity_elements.txt</a>,
the triangulation;
</li>
<li>
<a href = "../../datasets/triangulation_order3/big_cavity_triangulation.png">
big_cavity_triangulation.png</a>,
a PNG image of the triangulation;
</li>
<li>
<a href = "../../datasets/triangulation_order3/big_cavity_element_neighbors.txt">
big_cavity_element_neighbors.txt</a>,
the neighbor triangles.
</li>
</ul>
</p>
<p>
<b>BOX3</b> is a triangulation of order 3, using 20 nodes and 24 elements:
<ul>
<li>
<a href = "../../datasets/triangulation_order3/box3_nodes.txt">
box3_nodes.txt</a>,
the node coordinates.
</li>
<li>
<a href = "../../datasets/triangulation_order3/box3_elements.txt">
box3_elements.txt</a>,
the triangulation;
</li>
<li>
<a href = "../../datasets/triangulation_order3/box3_triangulation.png">
box3_triangulation.png</a>,
a PNG image of the triangulation;
</li>
<li>
<a href = "../../datasets/triangulation_order3/box3_element_neighbors.txt">
box3_element_neighbors.txt</a>,
the neighbor triangles.
</li>
</ul>
</p>
<p>
<b>BOX6</b> is a triangulation of order 6:
<ul>
<li>
<a href = "../../datasets/triangulation_order6/box6_nodes.txt">
box6_nodes.txt</a>,
the node coordinates.
</li>
<li>
<a href = "../../datasets/triangulation_order6/box6_elements.txt">
box6_elements.txt</a>,
the triangulation;
</li>
<li>
<a href = "../../datasets/triangulation_order6/box6_triangulation.png">
box6_triangulation.png</a>,
a PNG image the triangulation;
</li>
<li>
<a href = "../../datasets/triangulation_order6/box6_element_neighbors.txt">
box6_element_neighbors.txt</a>,
the neighbor triangles.
</li>
</ul>
</p>
<p>
<b>GREENLAND</b> is a triangulation using 33,343 nodes and 64,125 elements.
<ul>
<li>
<a href = "../../datasets/triangulation_order3/greenland_nodes.txt">
greenland_nodes.txt</a>,
the node coordinates.
</li>
<li>
<a href = "../../datasets/triangulation_order3/greenland_elements.txt">
greenland_elements.txt</a>,
the triangulation;
</li>
<li>
<a href = "../../datasets/triangulation_order3/greenland_element_neighbors.txt">
greenland_element_neighbors.txt</a>,
the neighbor triangles.
</li>
</ul>
</p>
<p>
<b>LAKE_COARSE</b> is an irregular lake with an island.<br>
There are 621 nodes and 974 elements and 1 hole.
<ul>
<li>
<a href = "lake_coarse_nodes.txt">lake_coarse_nodes.txt</a>,
the node coordinates.
</li>
<li>
<a href = "lake_coarse_elements.txt">lake_coarse_elements.txt</a>,
the triangulation;
</li>
<li>
<a href = "lake_coarse_triangulation.png">
lake_coarse_triangulation.png</a>,
a PNG image of the triangulation.
</li>
<li>
<a href = "lake_coarse_element_neighbors.txt">
lake_coarse_element_neighbors.txt</a>,
the neighbor triangles.
</li>
</ul>
</p>
<p>
<b>LAKE3</b> is an irregular lake with an island.<br>
The smallest angle is 23.46 degrees.<br>
There are 1552 nodes and 2820 elements and 1 hole.
<ul>
<li>
<a href = "lake3_nodes.txt">lake3_nodes.txt</a>,
the node coordinates.
</li>
<li>
<a href = "lake3_elements.txt">lake3_elements.txt</a>,
the triangulation;
</li>
<li>
<a href = "lake3_triangulation.png">lake3_triangulation.png</a>,
a PNG image of the triangulation.
</li>
<li>
<a href = "lake3_element_neighbors.txt">
lake3_element_neighbors.txt</a>,
the neighbor triangles.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 04 November 2010.
</i>
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